I understand the proof except for the following:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that -m_{2}< nx < m_{1}for positive integers m_{1}, m_{2}, n, and real number x.

Then there is an integer m with -m_{2}≤ m ≤ m_{1}such that m-1 ≤ nx < m.

It definitely sounds reasonable, but it seems like a big jump in logic.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Rudin Theorem 1.20 (b)

**Physics Forums | Science Articles, Homework Help, Discussion**